Problem: Rewrite as a simplified fraction. ${2.38\overline{3} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2383.3333...\\ 100x &= 238.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2145}$ ${x = \dfrac{2145}{900}} $ ${x = \dfrac{143}{60}} \text{or} {2 \dfrac{23}{60}}$